Accurate frequency estimation of a noisy sine-wave by means of an interpolated discrete-time Fourier transform algorithm
Accurate frequency estimation of a noisy sine-wave by means of an interpolated discrete-time Fourier transform algorithm
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DOI：
10.1016/j.measurement.2017.11.017
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发表时间：
2018-02-01
期刊：
影响因子：
5.6
通讯作者：
Dallet, Dominique
中科院分区：
文献类型：
--
作者：
Belega, Daniel;Petri, Dario;Dallet, Dominique
本文研究了最近提出的正弦波频率估计的精度的基础上插值的离散时间傅里叶变换（DTFT）频谱样本位于一个频率箱分开。具体地说，插值DTFT（IpDTFT）频率估计器的方差，由于加性宽带噪声的解析表达式推导出的情况下，当采集的正弦波样本加权的最大旁瓣衰减（MSD）窗口。推导出的表达式能够识别迭代算法，称为IpDTFT-NR过程，确保IpDTFT频率估计器的最大噪声抑制。此外，IpDTFT-NR程序的准确性进行了比较，另一种算法，称为IpDTFT-IR程序，它确保了最大的图像分量干扰抑制IpDTFT频率估计。为了这个目的，精确表达式的均方误差（MSE）的两个频率估计器。此外，IpDTFT-NR过程优于IpDTFT-IR过程的信噪比（SNR）的值被确定为所分析的正弦波周期的数量的函数。一旦已知或估计了分析信号的SNR和观察到的周期数，则该阈值的知识使得能够定义称为IpDTFT-IR/NR过程的算法，该算法通过使用上述两个过程中最准确的一个来估计正弦波频率。IpDTFT-IR/NR程序和其他国家的最先进的插值傅立叶算法的精度进行了比较，彼此使用模拟和实验数据。
This paper investigates the accuracy of a recently proposed sine-wave frequency estimator based on the interpolation of Discrete-Time Fourier Transform (DTFT) spectrum samples located one frequency bin apart. Specifically, an analytical expression for the variance of the Interpolated DTFT (IpDTFT) frequency estimator due to additive wide-band noise is derived in the case when the acquired sine-wave samples are weighted by a Maximum Sidelobe Decay (MSD) window. The derived expression enables the identification of an iterative algorithm, called IpDTFT-NR procedure, that ensures the maximum Noise Rejection on the IpDTFT frequency estimator. Moreover, the accuracy of the IpDTFT-NR procedure is compared with that of another algorithm, called IpDTFT-IR procedure, which ensures the maximum Image component interference Rejection on the IpDTFT frequency estimator. To this aim, accurate expressions for the Mean Square Errors (MSEs) of the two frequency estimators are derived. Also, the value of the Signal-to-Noise Ratio (SNR) up to which the IpDTFT-NR procedure outperforms the IpDTFT-IR one is determined as a function of the number of analysed sine-wave cycles. Once the SNR and the number of observed cycles of the analysed signal are known or estimated, the knowledge of this threshold enables the definition of an algorithm, called IpDTFT-IR/NR procedure, that estimates the sine-wave frequency by using the most accurate of the two procedures above. The accuracies of the IpDTFT-IR/NR procedure and of other state-of-the-art interpolated Fourier algorithms are compared with each other using both simulation and experimental data.